The generic stability of solutions for vector quasi-equilibrium problems on Hadamard manifolds

Abstract

In this paper, we first revisit two classes of set-valued vector quasi-equilibrium problems on Hadamard manifolds with established existence conditions of solutions in [9]. Then, we establish generic stability of set-valued mappings whose set of essential points of a map is a dense residual subset of a (Hausdorff) metric space of the set-valued maps. As applications, we study generalized vector quasi-variational-like inequalities and vector quasi-optimization problems on Hadamard manifolds.